Valuation on an Outside-Reset Option with Multiple Resettable Levels and Dates

<div>Option <svg height="8.68572pt" id="M241" style="vertical-align:-0.0498209pt" version="1.1" viewbox="-0.0498162 -8.6359 8.46388 8.68572" width="8.46388pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M600 0V24L339 665L311 657L43 24V0H600ZM497 50H107L303 539L497 50Z" id="g113-133"></path></g></svg> and <svg height="8.68572pt" id="M242" style="vertical-align:-0.0498209pt" version="1.1" viewbox="-0.0498162 -8.6359 6.71534 8.68572" width="6.71534pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M485 501C480 550 475 615 475 650H42V622C119 616 127 606 127 525V126C127 44 119 34 41 28V0H311V28C220 34 212 43 212 126V584C212 612 216 615 244 615H318C382 615 404 608 420 587C435 568 445 541 455 497L485 501Z" id="g113-132"></path></g></svg> at time <svg height="10.9953pt" id="M243" style="vertical-align:-3.18148pt" version="1.1" viewbox="-0.0498162 -7.81382 9.43046 10.9953" width="9.43046pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z" id="g113-117"></path></g><g transform="matrix(.0091,0,0,-0.0091,4.368,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path></g></svg> for different <span class="nowrap"><svg height="11.927pt" id="M244" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 12.1837 11.927" width="12.1837pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M640 650H413L406 622L438 617C475 611 483 605 463 571C422 503 346 400 296 333C264 403 215 529 199 575C189 604 191 614 228 618L262 622L271 650H30L23 622C90 615 97 609 119 553L212 321C222 295 223 285 218 259L193 127C176 39 167 33 82 28L76 0H350L356 28C266 36 257 40 275 127L303 266C308 290 314 302 328 322C396 418 454 493 498 546C551 610 565 616 631 622L640 650Z" id="g113-90"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.111,3.132)"><path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z" id="g50-49"></path></g></svg>.</span></div>

Complexity

fig5

Figure 5

Figure 5: Valuation on an Outside-Reset Option with Multiple Resettable Levels and Dates 